科研之友
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摘要
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment [-1, 1] with respect to a measure, or, more precisely, with respect to the functional mu(f) = mes{x is an element of [-1, 1]: vertical bar f(x)vertical bar >= 1}. We also discuss an analogous problem with respect to the integral functionals integral(1)(-1) phi (vertical bar f(x)vertical bar) dx for functions phi that are defined, nonnegative, and nondecreasing on the semiaxis [0, +infinity).
- 出版日期2010-10
